Q: What is the total or count of factors of the number 411,144?

 A: 32

How do I find the total factors of the number 411,144?

Step 1

Find the prime factorization of the number 411,144.

Use a factor tree to assist with solving. Take a look at our prime factorization page for additional help.

Factor Tree
411,144
Factor Arrows
2205,572
Factor Arrows
2102,786
Factor Arrows
251,393
Factor Arrows
317,131
Factor Arrows
37463

The prime factorization in exponential form is: 23 x 31 x 371 x 4631

Step 2

Setup the equation for determining the number of factors or divisors. The equation is:

d(n) = (a + 1)(b + 1)(c + 1)(d + 1)

Where d(n) is equal to the number of divisors of the number and a, b, etc. are equal to the exponents of the prime factorization.

Now substitute the letters in the equation with the the exponents of your prime factorization and then solve to calculate the total number of divisors.

411,144 = 23 x 31 x 371 x 4631
Down Arrow
d(n) = (a + 1)(b + 1)(c + 1)(d + 1)
Down Arrow
d(411144) = (3 + 1)(1 + 1)(1 + 1)(1 + 1)
Down Arrow
d(411144) = (4)(2)(2)(2)
Down Arrow
d(411144) = 32

More numbers for you to try

Take a look at the factors page to see the factors of 411,144 and how to find them.

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